Multicontinuum Wave Propagation in a Laminated Beam with Contrasting Stiffness and Density of Layers

Abstract

The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: e is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and ω is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters e2ω. If this value is small, then the limit model is the standard homogenized one-dimensional wave equation. On the contrary, if e2ω is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and “co-existing” at every point. The proof of these results uses the milticomponent homogenization method.